The National Unitary Institution "Belarusian State Institute of Metrology" (BelGIM)

Transcription

1 ЕВРО-АЗИАТСКОЕ СОТРУДНИЧЕСТВО ГОСУДАРСТВЕННЫХ МЕТРОЛОГИЧЕСКИХ УЧРЕЖДЕНИЙ (KOOMET) EURO-ASIAN COOPERATION OF NATIONAL METROLOGICAL INSTITUTIONS (COOMET) October 2017 The National Unitary Institution "Belarusian State Institute of Metrology" (BelGIM) SUPPLEMENTARY COMPARISON COOMET.L- S19 «Comparison of profiles of measuring bridges» COOMET Proect: 658/BY/15 COMPARISONS OF NATIONAL STANDARDS IN THE FIELD OF MEASUREMENTS OFDEVIATIONS FROM STRAIGHTNESS AND FLATNESS FINAL REPORT Pilot laboratory: Belarusian State Institute of Metrology (BelGIM) Contact person: V.B. Makarevich BelGIM Production and Research department for Measurements of Geometric Quantities , Starovilensky trakt, Minsk, 93, Republic of Belarus Fax

2 Contents Introduction.3 1 Comparison participants Organization of comparisons Transfer standards Procedure of measurements Ambient conditions during the comparisons Short description of measurement standards Comparison Procedure of evaluating the equivalence of the national standards included in the comparisons Resume Bibliography

3 Introduction The aim of the proect is to determine the degree of equivalence of national measurement standards of Belarus, Russia and Kazakhstan in the field of measurement of straightness and flatness deviations and to support the measurement capabilities claimed by the comparison participants. The comparison obtained are presented in Clause 7 of this Report. 1 Comparison participants Table 1 Comparison participants N o NMI Address NMI abbreviation Contact person , Telephone, Fax Vladimir Makarevich 1 National Unitary Institution "Belarusian State Institute of Metrology" 2 Federal State Unitary Enterprise Ural Research Institute for Metrology 93, Starovilensky trakt, Minsk, , Republic of Belarus 4 Krasnoarmeyskaya str., , Yekaterinburg, Russian Federation BelGIM UNIIM Yuriy Shimolin Tel./Fax: makarevich@belgim.by Tel.: +7 (343) Fax:: +7 (343) shimolin@uniim.ru 3 South- Kazakhstan Subsidiary of RSE Kazakhstan Institute of Metrology 83 Altynsarina str., Almaty, Republic of Kazakhstan SKS RSE KazInMetr Iryna Suvorova Tel.: +7 (327) Fax:+7 (327) metrology@nursat.kz 2 Organization of comparisons 2.1 The comparison principle is as follows: the comparison participants shall make tenfold measurements in 100-mm steps to determine profile straightness deviations of solid-stone bridges maintained at BelGIM, UNIIM and SKS RSE KazInMetr by using measuring instruments being the parts of their respective measurement standards. 2.2 Comparison scheme: round robin. 2.3 Pilot laboratory: BelGIM. 2.4 The comparisons are intended to: establish the degree of equivalence of measurement standards; validate the claimed CMC-data. 3

4 3 Transfer standards 3.1 During these comparisons, solid-stone bridges included in the national standards of the participant countries were applied as transfer standards. The basic technical characteristics thereof are given in the table 2. Table 2. Transfer standards NMI abbreviation BelGIM UNIIM SKS RSE KazInMetr Description of the measuring instrument Solid-stone bridge, special Solid-stone bridge, special Solid-stone bridge, special Nominal Technical remarks bridge length, L 3 m permanently installed on isolated footing 5 m permanently installed on isolated footing 4 m permanently installed on isolated footing Figure 1 Transfer Standard (BelGIM special solid-stone bridge) 4

5 Figure 2 Transfer Standard (UNIIM special solid-stone bridge) Figure 3 Transfer Standard (SKS RSE KazInMetr special solid-stone bridge) 4 Procedure of measurements 4.1 The measurement procedure is based on comparing the real shape of a profile or surface with that of a straight line or surface being reproduced by any available physical method. The physical principle of setting the reference line or surface might be a mechanical, gravitational or optical one. 5

6 4.2 When using standard bridges together with measurement systems intended for measuring the bridges straightness deviations, appropriate instructions for use shall be followed as specified in the relevant operation manuals. 4.3 It is the responsibility of the comparison participants to deliver their measurement systems to the place where the comparison is to be conducted. 4.4 The deviation of the profile from the straight line that connects its extreme points shall be determined stepwise. According to the proposed technique, the difference between the values of the function f(x) describing the profile under investigation shall be determined with respect to the terminal points of an interval the length of which is very small compared with the length of the surface to be measured. In that manner, the average slope of the profile is determined successively (step by step) at its partial sections. 4.5 Prior to performing measurements the standard bridges shall be thoroughly cleaned with alcohol and then wiped by a piece of dry lint-free cloth. 4.6 The deviation of the central section of the bridge working surface from the horizontal plane shall not exceed 0,01 mm/m when measured both longitudinally and transversely. Should the deviations from the horizontal plane be greater than 0,01 mm/m, the positioning of the standard bridge shall be adusted by appropriately changing the heights of its supports. If so, the measurements are allowed to be performed not earlier than 12 hours after completing the adustment. Presence of markings showing the points at which the measurements are to be performed during the comparisons shall be checked. The markings shall be applied at 100 mm intervals. The points shall be numbered sequentially as 0, 1, 2 N. 4.7 When measuring the straightness deviation using the step-by-step procedure, the surface profile slope shall be determined in succession (in steps) over the intervals [X k, X k+1 ], where k=0,1 n-1. For the purpose of further treatment of the observations the origin of the coordinates shall have been aligned with the reference horizontal plane. Then the value of the function f(x) describing the surface profile at the points with X k, k=0,1,, n coordinates shall be calculated by totalizing the measured data. 4.8 The determination of the deviation of the profile from the straight line that connects its extreme points shall be performed relative to the central crosssection of the bridge. 4.9 The value of the deviation from the straight line,, µm connecting the profile extreme points at the point k can be obtained by formula h k h k l ( k i 1 N k i k ), (1) N i 1 where k h is the deviation from the straight line connecting the extreme profile points at the point k during the -th measurement, µm ; l is the distance between the holders of the primary transducers of the measurement systems for measuring the standard, m; 6

7 i is the reading of the primary transducers of the measurement systems for measuring the standard (slope angle of the surface profile in the i-th section at the -th measurement), µm/m; is the number of the point at the bridge surface where the deviation from the straight line connecting the profile extreme points is being determined; N is the total number of the measured points at the bridge surface; is the specific measurement number. k 4.10 The deviation from straightness of the bridge of the measurement standard shall be calculated using the following formula H h max h min, (2) where Н is the straightness deviation of the measurement standard bridge, µm; h max is the largest absolute value of the positive deviation from the reference straight line over the whole length of the bridge of the measurement standard among all profile points measured, µm; h min is the largest absolute value of the negative deviation from the reference straight line over the whole length of the bridge of the measurement standard among all profile points measured, µm; 5 Ambient conditions during the comparisons 5.1 Ambient conditions at which the straightness deviations of the bridges were measured are stated in Table 3. Table 3 Ambient conditions Name of characteristic Allowable value Ambient temperature (20 2) С Relative air humidity 30 % to 70 % Temperature change rate, max. 0,5 С/h 6 Short description of measurement standards 6.1 The overall view of the measuring instruments included in the measurement standard of BelGIM is shown in Figure 4. 7

8 Figure 4 Overall view of the measurement system Electronic level meter WYLER maintained at BelGIM The BelGIM measurement system Electronic level meter WYLER comprises the following basic equipment manufactured by WYLER (Switzerland): - electronic gauge MINILEVEL NT No. 262/E0590; - electronic gauge MINILEVEL NT No. 263/11482; - level indicating device LEVELMETER 2000 No. E4015; - software: LEVELSOFT PRO. 6.2 The overall view of the measuring instruments included in the measurement standard of UNIIM is shown in Figure 6. Figure 5 Overall view of the measurement system Electronic level meter WYLER maintained at UNIIM The UNIIM measurement system Electronic level meter WYLER comprises the following basic equipment manufactured by WYLER (Switzerland): - electronic gauge BlueLEVEL NT No. Q0894; - electronic gauge BlueLEVEL NT No. Q0895; - electronic gauge BlueLEVEL NT No. Q0896; - electronic gauge BlueLEVEL NT No. Q0897; - level indicating device BlueMETER SIGMA No. Q1007; - level indicating device BlueMETER SIGMA No. Q1008; 8

9 - software: LEVELSOFT PRO. 6.3 The overall view of the measuring instruments included in the measurement standard of SKS RSE KazInMetr is shown in Figure 5. Figure 6 Overall view of the measurement system Electronic level meter WYLER maintained at SKS RSE KazInMetr The SKS RSE KazInMetr measurement system Electronic level meter WYLER comprises the following basic equipment manufactured by WYLER (Switzerland): - electronic gauge MINILEVEL NT No. G0748; - electronic gauge MINILEVEL NT No. L0765; - level indicating device LEVELMETER 2000 No. G04211; - software: LEVELSOFT PRO. 7 Comparison 7.1 Determining the values of the deviation from the straight line connecting the extreme points of the bridge profiles Mathematical treatment of the measurement obtained in the angle units to determine the values of the straightness deviations was performed in accordance with Formulae (1, 2). The measurement were processed in the Microsoft Excel program. The outcomes of the calculations are given in Tables Determination of the values of the deviation from the straight line connecting the extreme points of the BelGIM bridge profile Table 4 - The deviation from the straight line connecting the extreme points of the BelGIM bridge profile at each point of the bridge, obtained by means of the dedicated measuring system of Bel- GIM in µm Point number Deviation from the line connecting the extreme profile points mean of measurement Type A standard uncertainty 0 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 1-1,10-1,06-1,10-0,99-0,97-1,16-1,09-1,15-1,10-1,00-1,07 0,02 2-2,01-1,97-2,06-1,86-1,89-2,18-1,99-2,15-2,05-1,87-2,00 0,04 9

10 Point number Deviation from the line connecting the extreme profile points mean of measurement Type A standard uncertainty 3-2,84-2,79-2,93-2,68-2,70-3,10-2,81-3,05-2,91-2,67-2,85 0,05 4-4,25-4,16-4,35-4,04-4,06-4,54-4,19-4,50-4,31-4,01-4,24 0,06 5-5,55-5,41-5,64-5,32-5,29-5,85-5,45-5,88-5,68-5,27-5,53 0,07 6-6,05-5,79-6,07-5,68-5,67-6,26-5,82-6,31-6,09-5,64-5,94 0,08 7-6,05-5,75-6,05-5,62-5,65-6,24-5,78-6,35-6,07-5,60-5,91 0,09 8-5,60-5,22-5,51-5,10-5,13-5,75-5,27-5,85-5,57-5,05-5,41 0,09 9-4,55-4,06-4,39-4,03-3,98-4,65-4,11-4,75-4,43-3,92-4,29 0, ,61-3,02-3,36-3,04-3,00-3,69-3,08-3,71-3,42-2,91-3,28 0, ,87-2,21-2,58-2,25-2,22-2,85-2,25-2,92-2,59-2,08-2,48 0, ,36-1,70-2,04-1,74-1,66-2,28-1,71-2,36-2,04-1,52-1,94 0, ,17-1,50-1,82-1,57-1,46-2,09-1,46-2,13-1,84-1,32-1,74 0, ,21-1,48-1,81-1,56-1,43-2,08-1,43-2,09-1,83-1,35-1,73 0, ,34-1,61-1,97-1,70-1,59-2,20-1,55-2,21-2,01-1,52-1,87 0, ,31-1,52-1,88-1,64-1,53-2,14-1,45-2,10-1,92-1,48-1,80 0, ,28-1,50-1,86-1,65-1,55-2,14-1,42-2,06-1,89-1,49-1,78 0, ,26-1,44-1,82-1,65-1,53-2,09-1,37-2,00-1,86-1,48-1,75 0, ,36-1,56-1,91-1,80-1,65-2,18-1,51-2,08-1,94-1,62-1,86 0, ,57-1,83-2,18-2,09-1,93-2,42-1,75-2,32-2,20-1,92-2,12 0, ,73-2,03-2,34-2,28-2,13-2,59-1,94-2,50-2,38-2,15-2,31 0, ,82-2,15-2,44-2,40-2,23-2,66-2,07-2,55-2,49-2,27-2,41 0, ,89-2,25-2,52-2,52-2,34-2,70-2,19-2,63-2,60-2,34-2,50 0, ,85-2,27-2,47-2,55-2,34-2,68-2,23-2,57-2,63-2,34-2,49 0, ,82-2,29-2,44-2,57-2,37-2,67-2,27-2,53-2,62-2,40-2,50 0, ,69-2,22-2,33-2,50-2,29-2,53-2,17-2,42-2,52-2,36-2,40 0, ,40-1,94-2,08-2,27-2,06-2,24-1,95-2,11-2,24-2,12-2,14 0, ,88-1,57-1,65-1,80-1,67-1,77-1,55-1,66-1,74-1,70-1,70 0, ,12-0,93-0,99-0,88-1,00-1,03-0,94-0,98-1,03-1,00-0,99 0, ,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 h max 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 - h min -6,05-5,79-6,07-5,68-5,67-6,26-5,82-6,35-6,09-5,64-5,94 - Н 6,05 5,79 6,07 5,68 5,67 6,26 5,82 6,35 6,09 5,64 5,94 0,08 Table 5 - The deviation from the straight line connecting the extreme points of the BelGIM bridge profile at each point of the bridge, obtained by means of the dedicated measuring system of UNIIM in µm Point number Deviation from the line connecting the extreme profile point mean of measurement Type A standard uncertainty 0 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 1-0,71-0,87-0,82-0,87-0,79-0,92-0,90-0,85-0,72-0,63-0,81 0,03 2-1,68-1,67-1,67-1,73-1,71-1,80-1,70-1,72-1,54-1,48-1,67 0,03 3-2,61-2,40-2,40-2,50-2,59-2,57-2,55-2,51-2,34-2,30-2,48 0,03 4-4,17-3,99-4,05-4,13-4,22-4,23-4,25-4,16-3,92-3,92-4,10 0,04 5-5,48-5,25-5,36-5,35-5,56-5,50-5,47-5,42-5,17-5,18-5,37 0,04 6-6,04-5,65-5,83-5,77-6,06-6,01-6,02-5,89-5,60-5,66-5,85 0,06 7-6,08-5,64-5,83-5,82-6,14-6,10-6,10-5,93-5,60-5,72-5,90 0,06 8-5,59-5,14-5,31-5,31-5,64-5,57-5,60-5,41-5,01-5,22-5,38 0,07 9-4,72-4,22-4,31-4,30-4,70-4,58-4,68-4,45-4,02-4,09-4,41 0, ,76-3,23-3,35-3,29-3,75-3,63-3,75-3,49-3,04-3,18-3,45 0, ,01-2,49-2,60-2,50-2,99-2,94-3,02-2,70-2,26-2,42-2,69 0, ,49-2,03-2,06-1,98-2,54-2,49-2,56-2,24-1,75-1,91-2,21 0,09 10

11 Point number Deviation from the line connecting the extreme profile point mean of measurement Type A standard uncertainty 13-2,33-1,84-1,86-1,80-2,35-2,37-2,42-2,11-1,60-1,77-2,04 0, ,34-1,86-1,85-1,80-2,36-2,40-2,43-2,16-1,64-1,77-2,06 0, ,51-2,02-1,99-1,95-2,50-2,52-2,54-2,33-1,82-1,91-2,21 0, ,55-2,04-2,05-2,00-2,52-2,54-2,53-2,38-1,87-1,93-2,24 0, ,57-2,07-2,07-2,01-2,54-2,53-2,46-2,41-1,90-1,88-2,24 0, ,57-2,02-2,06-1,96-2,50-2,54-2,42-2,39-1,96-1,82-2,22 0, ,62-2,07-2,18-2,06-2,55-2,61-2,53-2,49-2,08-1,92-2,31 0, ,85-2,29-2,45-2,30-2,76-2,86-2,77-2,73-2,36-2,14-2,55 0, ,93-2,41-2,62-2,43-2,86-2,97-2,88-2,82-2,49-2,23-2,66 0, ,02-2,54-2,79-2,57-2,98-3,10-3,01-2,94-2,66-2,37-2,80 0, ,99-2,66-2,85-2,64-3,03-3,08-3,07-2,94-2,71-2,39-2,84 0, ,11-2,83-3,00-2,80-3,14-3,21-3,17-3,04-2,77-2,56-2,96 0, ,10-2,84-2,99-2,84-3,12-3,20-3,16-3,03-2,75-2,62-2,96 0, ,89-2,70-2,82-2,67-2,91-2,96-2,90-2,85-2,53-2,50-2,78 0, ,45-2,29-2,42-2,29-2,49-2,51-2,48-2,44-2,18-2,20-2,38 0, ,93-1,83-1,92-1,83-1,96-2,00-1,95-1,89-1,71-1,75-1,88 0, ,11-1,06-1,13-1,04-1,13-1,17-1,12-1,12-1,02-1,04-1,09 0, ,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 h max 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 - h min -6,08-5,65-5,83-5,82-6,14-6,10-6,10-5,93-5,60-5,72-5,90 - Н 6,08 5,65 5,83 5,82 6,14 6,10 6,10 5,93 5,60 5,72 5,90 0,06 Table 6 - The deviation from the straight line connecting the extreme points of the BelGIM bridge profile at each point of the bridge, obtained by means of the dedicated measuring system of SKS RSE KazInMetr in µm Point number Deviation from the line connecting the extreme profile point mean of measurement Type A standard uncertainty 0 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 1-1,11-0,99-1,10-1,03-1,13-1,14-1,10-0,96-1,03-1,05-1,06 0,02 2-2,08-1,85-2,05-1,87-2,11-2,08-2,00-1,83-1,90-1,94-1,97 0,03 3-2,94-2,61-2,87-2,65-2,91-2,92-2,81-2,62-2,65-2,72-2,77 0,04 4-4,39-3,93-3,65-4,09-4,28-4,32-4,19-3,99-4,07-4,12-4,10 0,07 5-5,66-5,14-4,96-5,29-5,54-5,59-5,44-5,25-5,32-5,35-5,35 0,07 6-6,10-5,49-5,36-5,66-5,95-5,97-5,83-5,63-5,69-5,73-5,74 0,07 7-6,09-5,39-5,28-5,59-5,94-5,92-5,77-5,69-5,61-5,68-5,70 0,08 8-5,58-4,79-4,75-5,01-5,38-5,42-5,24-5,16-5,04-5,15-5,15 0,08 9-4,48-3,63-3,64-3,82-4,25-4,31-4,11-4,06-3,91-4,06-4,03 0, ,52-2,59-2,66-2,82-3,30-3,33-3,14-3,00-2,92-3,07-3,03 0, ,73-1,77-1,85-1,95-2,52-2,51-2,34-2,21-2,08-2,30-2,23 0, ,26-1,24-1,34-1,47-1,99-1,99-1,82-1,64-1,55-1,82-1,71 0, ,10-1,04-1,14-1,20-1,80-1,77-1,60-1,39-1,34-1,64-1,50 0, ,13-1,01-1,15-1,17-1,76-1,73-1,58-1,36-1,33-1,63-1,48 0, ,29-1,14-1,30-1,31-1,90-1,86-1,72-1,48-1,51-1,79-1,63 0, ,24-1,06-1,25-1,24-1,79-1,77-1,65-1,40-1,41-1,72-1,55 0, ,29-1,06-1,26-1,23-1,77-1,76-1,62-1,39-1,39-1,69-1,55 0, ,24-1,02-1,19-1,16-1,73-1,68-1,55-1,38-1,32-1,64-1,49 0, ,35-1,15-1,35-1,32-1,85-1,74-1,70-1,47-1,43-1,76-1,61 0, ,37-1,44-1,68-1,57-2,09-1,97-1,96-1,74-1,70-2,03-1,86 0, ,56-1,63-1,90-1,73-2,27-2,12-2,16-1,92-1,86-2,22-2,04 0,09 11

12 Point number Deviation from the line connecting the extreme profile point mean of measurement Type A standard uncertainty 22-2,68-1,80-1,85-1,89-2,37-2,25-2,27-2,04-2,02-2,31-2,15 0, ,71-1,92-1,99-1,97-2,42-2,30-2,34-2,14-2,13-2,37-2,23 0, ,69-2,00-2,06-2,16-2,44-2,31-2,41-2,12-2,18-2,40-2,28 0, ,64-2,07-2,12-2,18-2,40-2,30-2,44-2,13-2,19-2,38-2,28 0, ,55-2,06-2,10-2,15-2,33-2,25-2,43-2,09-2,15-2,31-2,24 0, ,22-1,85-1,87-1,90-2,02-1,97-2,22-1,85-1,90-2,05-1,99 0, ,76-1,52-1,53-1,47-1,60-1,57-1,86-1,51-1,51-1,62-1,59 0, ,06-0,82-0,93-0,90-0,92-0,91-1,26-0,91-0,90-0,95-0,95 0, ,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 h max 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 - h min -6,10-5,49-5,36-5,66-5,95-5,97-5,83-5,69-5,69-5,73-5,75 - Н 6,10 5,49 5,36 5,66 5,95 5,97 5,83 5,69 5,69 5,73 5,75 0, Determination of the values of the deviation from the straight line connecting the extreme points of the UNIIM bridge profile Table 7 - The deviation from the straight line connecting the extreme points of the UNIIM bridge profile at each point of the bridge, obtained by means of the dedicated measuring system of Bel- GIM in µm Point number Deviation from the line connecting the extreme profile point mean of measurement 0 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 1 0,65 0,53 0,61 0,74 0,72 0,77 0,72 0,72 0,83 0,63 0,69 0,03 2 1,11 0,91 1,10 1,31 1,26 1,34 1,25 1,26 1,45 1,12 1,21 0,05 3 2,15 1,84 2,14 2,44 2,37 2,49 2,33 2,36 2,65 2,18 2,29 0,07 4 2,89 2,43 2,87 3,21 3,12 3,28 3,07 3,13 3,47 2,88 3,03 0,09 5 3,76 3,06 3,62 4,04 3,94 4,12 3,87 3,96 4,36 3,65 3,84 0,11 6 5,06 4,32 4,99 5,47 5,36 5,57 5,28 5,39 5,82 5,00 5,22 0,12 7 6,67 5,72 6,55 7,10 6,98 7,19 6,87 7,00 7,48 6,51 6,81 0,14 8 8,44 7,32 8,28 8,92 8,75 9,00 8,66 8,78 9,28 8,21 8,56 0, ,23 8,95 10,02 10,73 10,55 10,79 10,44 10,58 11,10 9,91 10,33 0, ,56 10,10 11,23 12,06 11,83 12,10 11,75 11,91 12,40 11,10 11,60 0, ,89 11,20 12,45 13,08 13,11 13,40 13,03 13,22 13,62 12,25 12,82 0, ,18 12,29 13,61 14,32 14,33 14,66 14,28 14,46 14,89 13,36 14,04 0, ,39 13,34 14,73 15,55 15,52 15,87 15,48 15,70 16,09 14,43 15,21 0, ,59 14,30 15,80 16,69 16,64 17,02 16,58 16,82 17,21 15,41 16,31 0, ,85 15,38 16,94 17,92 17,83 18,24 17,78 18,04 18,40 16,48 17,49 0, ,01 16,33 18,01 19,03 18,92 19,33 18,87 19,16 19,45 17,47 18,56 0, ,79 16,92 18,71 19,80 19,66 20,11 19,62 19,95 20,13 18,10 19,28 0, ,16 17,10 18,97 20,10 19,99 20,44 19,94 20,28 20,37 18,32 19,57 0, ,57 17,45 19,33 20,49 20,37 20,82 20,34 20,71 20,70 18,61 19,94 0, ,67 17,40 19,37 20,54 20,39 20,84 20,37 20,78 20,69 18,56 19,96 0, ,37 17,01 19,04 20,20 20,07 20,52 20,03 20,48 20,39 18,17 19,63 0, ,36 16,92 19,01 20,18 20,03 20,49 19,98 20,45 20,33 18,09 19,58 0, ,85 16,40 18,54 19,70 19,56 19,99 19,52 19,98 19,88 17,59 19,10 0, ,45 16,02 18,17 19,33 19,19 19,62 19,13 19,60 19,51 17,20 18,72 0, ,93 15,52 17,69 18,83 18,69 19,12 18,60 19,09 19,03 16,70 18,22 0, ,55 15,18 17,39 18,47 18,33 18,74 18,25 18,73 18,73 16,35 17,87 0, ,25 14,98 17,18 18,21 18,09 18,50 17,99 18,48 18,54 16,16 17,64 0, ,21 15,03 17,23 18,24 18,09 18,53 18,01 18,51 18,60 16,24 17,67 0, ,97 14,95 17,15 18,10 17,95 18,38 17,88 18,37 18,50 16,17 17,54 0, ,80 14,89 17,08 17,96 17,83 18,23 17,79 18,27 18,43 16,12 17,44 0,34 Type A standard uncertainty 12

13 Point number Deviation from the line connecting the extreme profile point mean of meas- Type A standard uncertainty urement 31 17,62 14,85 17,01 17,81 17,71 18,07 17,67 18,14 18,31 16,06 17,32 0, ,27 14,62 16,76 17,47 17,43 17,74 17,39 17,85 18,06 15,84 17,04 0, ,57 14,09 16,21 16,85 16,83 17,08 16,75 17,23 17,43 15,32 16,43 0, ,48 13,11 15,25 15,81 15,79 16,03 15,70 16,15 16,38 14,39 15,41 0, ,24 11,97 14,10 14,58 14,60 14,80 14,49 14,92 15,19 13,46 14,24 0, ,41 10,24 12,33 12,79 12,79 12,98 12,68 13,10 13,39 11,78 12,45 0, ,58 8,54 10,55 10,96 10,95 11,12 10,86 11,27 11,56 10,08 10,65 0, ,61 6,66 8,63 9,01 8,97 9,16 8,92 9,27 9,61 8,24 8,71 0, ,09 6,09 7,17 7,49 7,48 7,62 7,38 7,74 8,09 6,87 7,30 0, ,51 4,47 5,60 5,90 5,91 6,01 5,81 6,10 6,47 5,41 5,72 0, ,33 3,47 4,43 4,64 4,70 4,80 4,59 4,86 5,21 4,31 4,53 0, ,51 2,69 3,61 3,79 3,88 3,95 3,74 3,99 4,36 3,61 3,71 0, ,07 2,29 3,16 3,25 3,40 3,45 3,24 3,44 3,86 3,26 3,24 0, ,59 1,91 2,72 2,75 2,93 2,86 2,75 2,93 3,29 2,91 2,76 0, ,71 1,07 1,86 1,85 2,01 1,95 1,85 1,98 2,33 2,09 1,87 0, ,94 0,65 1,09 1,12 1,23 1,19 1,11 1,19 1,47 1,43 1,14 0, ,15-0,11 0,27 0,35 0,36 0,37 0,28 0,39 0,56-0,27 0,23 0, ,34-0,45-0,23-0,15-0,16-0,16-0,20-0,13-0,04-0,61-0,25 0, ,26-0,32-0,21-0,17-0,19-0,20-0,21-0,16-0,09-0,41-0,22 0, ,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 h max 20,67 17,45 19,37 20,54 20,39 20,84 20,37 20,78 20,70 18,61 19,96 - h min -0,34-0,45-0,23-0,17-0,19-0,20-0,21-0,16-0,09-0,61-0,25 - Н 21,01 17,90 19,60 20,72 20,58 21,04 20,58 20,95 20,80 19,23 20,21 0,31 Table 8 - The deviation from the straight line connecting the extreme points of the UNIIM bridge profile at each point of the bridge, obtained by means of the dedicated measuring system of UNIIM in µm Poin t num ber Deviation from the line connecting the extreme profile point mean of measurement Type A standard uncertainty 0 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 1 0,63 0,10 0,74 0,73 0,26 0,55 0,47 0,08 0,63 0,48 0,47 0,07 2 1,01 0,51 1,21 1,23 0,91 1,08 1,14 0,72 1,20 0,94 0,99 0,07 3 1,97 1,48 2,30 2,32 2,01 2,15 2,32 1,75 2,31 2,06 2,07 0,08 4 2,68 2,18 3,20 3,06 2,83 2,95 3,09 2,54 3,11 2,95 2,86 0,09 5 3,20 2,72 3,90 3,67 3,45 3,63 3,83 3,00 3,55 3,62 3,46 0,11 6 4,25 3,91 5,12 4,90 4,75 4,93 5,14 4,37 4,83 5,01 4,72 0,12 7 5,69 5,32 6,67 6,46 6,29 6,47 6,65 5,88 6,30 6,55 6,23 0,14 8 7,37 7,04 8,49 8,28 8,14 8,33 8,55 7,69 8,08 8,40 8,04 0,15 9 9,01 8,69 10,09 9,98 9,86 10,14 10,32 9,38 9,71 10,19 9,74 0, ,25 9,97 11,37 11,28 11,11 11,53 11,70 10,62 10,93 11,54 11,03 0, ,41 11,10 12,59 12,51 12,15 12,83 13,02 11,85 12,03 12,78 12,23 0, ,60 12,32 13,82 13,75 13,42 14,19 14,34 13,06 13,24 14,03 13,48 0, ,72 13,48 15,00 14,99 14,55 15,41 15,58 14,22 14,34 15,06 14,64 0, ,94 14,58 16,11 16,14 15,61 16,56 16,65 15,38 15,38 16,03 15,74 0, ,03 15,64 17,12 17,27 16,49 17,74 17,64 16,48 16,37 17,15 16,79 0, ,01 16,61 18,07 18,28 17,37 18,81 18,57 17,42 17,23 18,14 17,75 0, ,71 17,30 18,72 18,95 17,94 19,50 19,22 18,08 17,83 18,83 18,41 0, ,08 17,61 19,03 19,28 18,24 19,70 19,55 18,39 18,14 19,18 18,72 0, ,58 17,98 19,41 19,70 18,55 20,08 19,91 18,72 18,51 19,44 19,09 0, ,68 18,04 19,50 19,73 18,60 20,15 20,08 18,74 18,63 19,41 19,16 0, ,43 17,78 19,25 19,43 18,20 19,93 19,88 18,43 18,41 19,17 18,89 0, ,35 17,66 18,92 19,27 17,95 19,81 19,73 18,22 18,34 19,08 18,73 0, ,89 17,24 18,50 18,81 17,34 19,42 19,35 17,79 18,01 18,59 18,29 0, ,57 16,90 18,11 18,32 16,82 19,03 18,98 17,49 17,62 18,20 17,90 0,23 13

14 Poin t num ber Deviation from the line connecting the extreme profile point mean of measurement 25 17,20 16,46 17,68 17,86 16,25 18,57 18,55 16,91 17,16 17,70 17,43 0, ,83 16,09 17,32 17,40 15,72 18,20 18,21 16,53 16,88 17,33 17,05 0, ,52 15,93 17,15 17,17 15,43 18,02 18,05 15,78 16,43 17,14 16,76 0, ,60 16,00 17,20 17,12 15,39 18,05 18,04 15,87 16,42 17,23 16,79 0, ,58 16,04 17,24 17,15 15,19 17,96 18,03 15,93 16,38 17,22 16,77 0, ,55 15,95 17,19 17,11 15,00 17,88 17,98 15,86 16,28 17,19 16,70 0, ,51 15,86 17,13 17,03 14,93 17,73 17,90 15,67 16,18 17,11 16,60 0, ,24 15,59 16,77 16,70 14,68 17,35 17,58 15,38 15,82 16,71 16,28 0, ,89 15,16 16,31 16,26 14,30 16,84 16,96 14,99 15,45 16,18 15,83 0, ,98 14,15 15,27 15,23 13,36 15,83 15,94 13,22 14,46 15,12 14,76 0, ,88 13,00 14,05 14,04 12,21 14,41 14,60 12,04 13,24 13,87 13,53 0, ,84 11,33 12,30 12,35 10,61 12,63 12,89 10,42 11,54 12,20 11,81 0, ,98 9,63 10,51 10,59 9,01 10,81 11,09 8,89 9,88 10,51 10,09 0, ,03 7,78 8,64 8,71 7,27 8,96 9,25 7,15 8,01 8,68 8,25 0, ,26 6,17 7,02 7,07 5,66 7,23 7,53 5,67 6,42 7,03 6,60 0, ,54 4,62 5,42 5,47 4,17 5,60 5,85 4,23 4,90 5,44 5,02 0, ,14 3,47 4,21 4,26 3,10 4,35 4,59 3,20 3,75 4,18 3,83 0, ,41 2,80 3,54 3,57 2,49 3,53 3,89 2,60 3,14 3,41 3,14 0, ,96 2,29 3,03 3,06 2,07 2,96 3,18 2,19 2,63 2,90 2,63 0, ,74 2,06 2,72 2,71 1,86 2,70 2,79 2,09 2,43 2,61 2,37 0, ,95 1,23 1,77 1,77 1,09 1,78 1,94 1,31 1,63 1,77 1,52 0, ,33 0,54 0,98 0,97 0,43 0,98 1,10 0,62 0,87 0,95 0,78 0, ,26-0,15 0,23 0,24-0,14 0,20 0,35 0,00 0,20 0,24 0,09 0, ,58-0,51-0,25-0,24-0,51-0,29-0,20-0,40-0,28-0,30-0,36 0, ,44-0,39-0,27-0,25-0,40-0,27-0,28-0,27-0,25-0,26-0,31 0, ,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 h max 18,68 18,04 19,50 19,73 18,60 20,15 20,08 18,74 18,63 19,44 19,16 - h min -0,58-0,51-0,27-0,25-0,51-0,29-0,28-0,40-0,28-0,30-0,36 - Н 19,26 18,55 19,76 19,99 19,11 20,44 20,36 19,14 18,91 19,74 19,51 0,19 Table 9 - The deviation from the straight line connecting the extreme points of the UNIIM bridge profile at each point of the bridge, obtained by means of the dedicated measuring system of SKS RSE KazInMetr in µm Point num ber Deviation from the line connecting the extreme profile point Type A standard uncertainty mean of measurement Type A standard uncertainty 0 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 1 0,64 0,56 0,64 0,74 0,63 0,63 0,74 0,61 0,47 0,56 0,62 0,02 2 1,08 1,00 1,12 1,33 1,16 1,14 1,30 1,07 0,82 0,96 1,10 0,05 3 1,98 1,90 2,10 2,40 2,18 2,15 2,44 2,12 1,71 1,93 2,09 0,07 4 2,57 2,53 2,75 3,14 2,85 2,85 3,25 2,83 2,31 2,53 2,76 0,09 5 3,29 3,21 3,45 3,93 3,60 3,60 4,08 3,59 2,94 3,21 3,49 0,10 6 4,49 4,43 4,73 5,28 4,91 4,92 5,51 4,94 4,17 4,49 4,79 0,12 7 5,96 5,92 6,27 6,88 6,45 6,46 7,15 6,49 5,58 5,96 6,31 0,14 8 7,57 7,54 7,95 8,64 8,14 8,17 8,92 8,19 7,17 7,62 7,99 0,16 9 9,28 9,28 9,69 10,46 9,91 9,94 10,72 9,91 8,78 9,32 9,73 0, ,47 10,51 10,94 11,75 11,21 11,22 12,01 11,13 9,93 10,54 10,97 0, ,64 11,68 12,16 13,26 12,42 12,44 13,27 12,31 11,09 11,71 12,20 0, ,75 12,83 13,35 14,51 13,61 13,64 14,50 13,47 12,15 12,86 13,37 0, ,87 13,96 14,52 15,67 14,80 14,81 15,79 14,70 13,23 14,00 14,54 0, ,94 15,05 15,67 16,90 15,95 16,43 16,91 15,74 14,22 15,07 15,69 0, ,05 16,19 16,86 18,09 17,10 17,62 18,12 16,90 15,37 16,19 16,85 0,27 14

15 Point num ber Deviation from the line connecting the extreme profile point mean of measurement Type A standard uncertainty 16 17,12 17,29 18,00 19,26 18,23 18,73 19,23 17,96 16,39 17,23 17,94 0, ,77 17,96 18,71 20,01 18,92 19,43 19,95 18,59 17,06 17,92 18,63 0, ,94 18,18 19,00 20,34 19,19 19,74 20,21 18,83 17,31 18,14 18,89 0, ,26 18,55 19,42 20,79 19,59 20,14 20,61 19,14 17,66 18,49 19,26 0, ,20 18,53 19,43 20,83 19,59 20,15 20,61 19,28 17,61 18,50 19,27 0, ,81 18,16 19,10 20,57 19,23 19,79 20,21 18,91 17,25 18,17 18,92 0, ,74 18,10 19,12 20,55 19,14 19,69 20,11 18,77 17,12 18,07 18,84 0, ,24 17,60 18,60 20,06 18,61 19,16 19,60 18,20 16,59 17,54 18,32 0, ,84 17,19 18,18 19,66 18,16 18,74 19,15 17,74 16,16 17,12 17,89 0, ,37 16,73 17,66 19,17 17,64 18,21 18,62 17,27 15,58 16,57 17,38 0, ,05 16,40 17,29 18,82 17,26 17,82 18,26 16,86 15,22 16,21 17,02 0, ,81 16,22 17,05 18,54 17,03 17,56 17,99 16,59 14,99 15,98 16,77 0, ,86 16,30 17,05 18,56 17,06 17,57 18,00 16,62 15,05 16,03 16,81 0, ,70 16,17 16,88 18,39 16,89 17,39 17,83 16,48 14,93 15,92 16,66 0, ,58 16,08 16,75 18,23 16,78 17,23 17,67 16,32 14,81 15,80 16,52 0, ,47 15,99 16,61 18,08 16,67 17,08 17,53 16,18 14,68 15,70 16,40 0, ,24 15,75 16,34 17,81 16,41 16,78 17,22 15,91 14,44 15,46 16,14 0, ,66 15,10 15,66 17,13 15,75 16,14 16,60 15,29 13,84 14,87 15,50 0, ,67 14,11 14,67 16,10 14,75 15,12 15,63 14,31 13,66 13,93 14,59 0, ,53 12,99 13,52 14,93 13,61 13,94 14,45 13,15 12,52 12,80 13,44 0, ,79 11,23 11,75 13,14 11,86 12,15 12,66 11,42 10,80 11,12 11,69 0, ,04 9,51 10,09 11,28 10,11 10,37 10,87 9,66 9,10 9,41 9,94 0, ,16 7,61 8,14 9,31 8,18 8,42 8,88 7,77 7,25 7,54 8,03 0, ,78 6,18 6,66 7,77 6,70 6,92 7,37 6,32 5,82 6,10 6,56 0, ,34 4,72 5,16 6,22 5,19 5,36 5,79 4,85 4,38 4,65 5,06 0, ,16 3,53 3,93 4,93 3,96 4,15 4,54 3,68 3,26 3,51 3,87 0, ,43 2,77 3,13 4,05 3,16 3,43 3,70 2,94 2,55 2,79 3,10 0, ,12 2,40 2,74 3,56 2,74 2,96 3,21 2,53 2,19 2,40 2,68 0, ,70 1,93 2,26 3,00 2,31 2,47 2,70 2,12 1,82 2,00 2,23 0, ,98 1,16 1,46 2,09 1,50 1,63 1,81 1,35 1,08 1,26 1,43 0, ,38 0,55 0,78 1,28 0,82 0,91 1,08 0,71 0,47 0,62 0,76 0, ,30-0,18 0,02 0,40 0,05 0,18 0,23-0,02-0,22-0,08 0,01 0, ,59-0,52-0,36-0,12-0,36-0,28-0,24-0,42-0,53-0,45-0,39 0, ,32-0,27-0,23-0,09-0,22-0,20-0,21-0,29-0,35-0,32-0,25 0, ,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 h max 18,26 18,55 19,43 20,83 19,59 20,15 20,61 19,28 17,66 18,50 19,27 - h min -0,59-0,52-0,36-0,12-0,36-0,28-0,24-0,42-0,53-0,45-0,39 - Н 18,85 19,07 19,80 20,95 19,94 20,44 20,85 19,70 18,19 18,95 19,66 0,27 15

16 7.1.3 Determination of the values of the deviation from the straight line connecting the extreme points of the SKS RSE KazInMetr bridge profile Table 10 - The deviation from the straight line connecting the extreme points of the SKS RSE KazInMetr bridge profile at each point of the bridge, obtained by means of the dedicated measuring system of BelGIM Point number Deviation from the line connecting the extreme profile point mean of measurement in µm Type A standard uncertainty 0 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 1-0,04 0,00 0,10 0,22 0,21-0,08 0,02 0,18 0,29-0,03 0,09 0,04 2-0,26-0,19 0,03 0,27 0,19-0,34-0,11 0,13 0,31-0,28-0,03 0,08 3 0,87 0,98 1,30 1,68 1,58 0,72 1,06 1,45 1,75 0,89 1,23 0,12 4 0,91 0,96 1,44 1,94 1,81 0,72 1,12 1,64 2,01 0,85 1,34 0,15 5 1,13 1,19 1,80 2,41 2,21 0,90 1,40 2,04 2,50 1,00 1,66 0,19 6 1,11 1,18 1,86 2,62 2,36 0,88 1,40 2,20 2,68 0,88 1,72 0,23 7 1,03 1,10 1,89 2,73 2,44 0,79 1,36 2,29 2,81 0,74 1,72 0,26 8 0,82 0,88 1,75 2,70 2,38 0,56 1,21 2,22 2,80 0,46 1,58 0,29 9 0,45 0,52 1,44 2,50 2,13 0,19 0,90 1,98 2,61 0,03 1,28 0, ,00 0,08 1,08 2,22 1,83-0,26 0,55 1,71 2,34-0,46 0,91 0, ,16-0,05 1,03 2,20 1,81-0,41 0,49 1,72 2,37-0,61 0,84 0, ,39-0,26 0,91 2,10 1,68-0,61 0,31 1,63 2,23-0,91 0,67 0, ,52-0,35 0,86 2,12 1,71-0,72 0,26 1,61 2,23-1,08 0,61 0, ,63-0,41 0,81 2,13 1,72-0,78 0,24 1,56 2,17-1,23 0,56 0, ,40-0,23 1,12 2,44 1,99-0,56 0,54 1,84 2,44-1,05 0,81 0, ,00 0,16 1,54 2,87 2,45-0,14 1,00 2,30 2,84-0,69 1,23 0, ,32 0,49 1,92 3,22 2,85 0,31 1,36 2,64 3,20-0,38 1,59 0, ,68 0,86 2,30 3,60 3,21 0,64 1,72 3,03 3,52-0,05 1,95 0, ,88 1,04 2,44 3,77 3,33 0,74 1,93 3,17 3,62 0,10 2,10 0, ,79 0,95 2,36 3,70 3,20 0,63 1,86 3,01 3,55 0,01 2,01 0, ,01 1,15 2,49 3,87 3,31 0,79 2,03 3,12 3,68 0,13 2,16 0, ,38 1,51 2,79 4,20 3,59 1,11 2,38 3,43 3,96 0,46 2,48 0, ,74 1,82 3,14 4,52 3,87 1,42 2,71 3,69 4,24 0,77 2,79 0, ,97 2,01 3,26 4,65 3,98 1,57 2,91 3,81 4,36 0,94 2,94 0, ,21 2,17 3,35 4,70 4,05 1,69 3,06 3,90 4,43 1,09 3,07 0, ,97 1,94 3,05 4,36 3,73 1,42 2,80 3,58 4,09 0,86 2,78 0, ,29 1,24 2,32 3,58 2,97 0,71 2,11 2,82 3,30 0,19 2,05 0, ,44 0,39 1,45 2,67 2,06-0,13 1,23 1,91 2,36-0,66 1,17 0, ,51-0,58 0,43 1,62 1,03-1,09 0,26 0,87 1,25-1,61 0,17 0, ,44-1,54-0,58 0,59 0,01-2,02-0,75-0,17 0,19-2,54-0,82 0, ,52-2,60-1,73-0,59-1,16-3,06-1,84-1,36-1,00-3,55-1,94 0, ,33-3,44-2,61-1,56-2,13-3,87-2,74-2,29-1,96-4,26-2,82 0, ,69-3,85-3,11-2,17-2,66-4,26-3,18-2,81-2,50-4,59-3,28 0, ,41-3,55-2,90-2,07-2,51-3,83-2,94-2,60-2,39-4,19-3,04 0, ,01-3,13-2,57-1,89-2,25-3,33-2,59-2,33-2,13-3,66-2,69 0, ,55-2,66-2,17-1,63-1,93-2,81-2,08-1,99-1,82-3,09-2,27 0, ,19-2,24-1,89-1,47-1,69-2,31-1,85-1,74-1,63-2,61-1,96 0, ,62-1,65-1,40-1,12-1,25-1,71-1,35-1,36-1,17-1,91-1,45 0, ,59-0,62-0,51-0,39-0,44-0,63-0,44-0,46-0,39-0,77-0,52 0, ,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 h max 2,21 2,17 3,35 4,70 4,05 1,69 3,06 3,90 4,43 1,09 3,07 - h min -3,69-3,85-3,11-2,17-2,66-4,26-3,18-2,81-2,50-4,59-3,28 - Н 5,91 6,02 6,46 6,87 6,71 5,95 6,24 6,71 6,94 5,68 6,35 0,14 16

17 Table 11 - The deviation from the straight line connecting the extreme points of the SKS RSE KazInMetr bridge profile at each point of the bridge, obtained by means of the dedicated measuring system of UNIIM in µm Point number Deviation from the line connecting the extreme profile point mean of measurement Type A standard uncertainty 0 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 1-0,18-0,08-0,22-0,05 0,08-0,21 0,00-0,04-0,14 0,06-0,08 0,03 2-0,46-0,32-0,56-0,25 0,00-0,57-0,22-0,19-0,32-0,04-0,29 0,06 3 0,71 0,91 0,59 0,93 1,34 0,56 0,94 1,15 0,93 1,31 0,94 0,09 4 0,71 1,00 0,54 1,04 1,54 0,52 1,02 1,30 1,01 1,51 1,02 0,11 5 0,94 1,29 0,80 1,29 1,92 0,66 1,29 1,63 1,28 1,86 1,30 0,13 6 0,65 1,08 0,52 1,13 1,91 0,39 1,14 1,56 1,14 1,88 1,14 0,17 7 0,46 0,94 0,34 1,07 1,95 0,23 0,95 1,52 1,02 1,84 1,03 0,19 8 0,11 0,65 0,00 0,77 1,78-0,17 0,62 1,32 0,81 1,63 0,75 0,21 9-0,31 0,34-0,38 0,44 1,55-0,55 0,26 1,04 0,56 1,39 0,43 0, ,81-0,14-0,88-0,10 1,10-1,06-0,31 0,60 0,14 0,97-0,05 0, ,96-0,20-0,97-0,23 1,10-1,17-0,39 0,55 0,18 1,00-0,11 0, ,39-0,53-1,34-0,55 0,77-1,52-0,73 0,23-0,07 0,75-0,44 0, ,61-0,74-1,56-0,72 0,62-1,73-0,91 0,05-0,22 0,62-0,62 0, ,68-0,78-1,64-0,77 0,62-1,81-0,93 0,03-0,22 0,60-0,66 0, ,53-0,59-1,45-0,57 0,86-1,67-0,74 0,25 0,00 0,81-0,46 0, ,09-0,13-1,07-0,12 1,37-1,23-0,33 0,74 0,50 1,30-0,01 0, ,92 0,06-0,85 0,08 1,57-1,05-0,13 0,99 0,77 1,53 0,20 0, ,60 0,40-0,46 0,48 1,93-0,68 0,24 1,32 1,15 1,90 0,57 0, ,48 0,54-0,36 0,62 2,12-0,48 0,43 1,53 1,37 2,05 0,73 0, ,41 0,60-0,28 0,73 2,15-0,42 0,47 1,56 1,56 2,14 0,81 0, ,16 0,86-0,05 0,96 2,34-0,14 0,69 1,80 1,81 2,37 1,05 0, ,10 1,12 0,23 1,27 2,56 0,14 0,95 2,05 2,10 2,63 1,32 0, ,35 1,37 0,49 1,56 2,78 0,47 1,25 2,32 2,40 2,88 1,59 0, ,62 1,62 0,76 1,82 2,97 0,72 1,46 2,52 2,63 3,06 1,82 0, ,76 1,79 0,86 1,90 3,00 0,88 1,62 2,60 2,80 3,16 1,94 0, ,56 1,54 0,70 1,64 2,71 0,66 1,36 2,31 2,52 2,84 1,68 0, ,10 0,84 0,03 0,97 1,99 0,03 0,70 1,58 1,85 2,22 1,01 0, ,85 0,11-0,68 0,20 1,16-0,71-0,08 0,76 1,00 1,41 0,23 0, ,77-0,86-1,62-0,76 0,14-1,58-1,04-0,22 0,05 0,45-0,72 0, ,62-1,79-2,43-1,70-0,81-2,44-1,98-1,17-0,90-0,60-1,64 0, ,64-2,86-3,51-2,81-1,95-3,42-3,05-2,29-2,01-1,75-2,73 0, ,47-3,77-4,34-3,69-2,88-4,25-3,92-3,23-2,94-2,73-3,62 0, ,77-4,13-4,65-4,09-3,35-4,54-4,23-3,62-3,31-3,13-3,98 0, ,40-3,89-4,32-3,83-3,19-4,21-3,92-3,42-3,11-2,96-3,73 0, ,89-3,44-3,86-3,30-2,89-3,69-3,37-2,95-2,72-2,57-3,27 0, ,33-2,96-3,32-2,89-2,53-3,26-3,01-2,66-2,41-2,24-2,86 0, ,86-2,48-2,77-2,45-2,12-2,74-2,51-2,25-2,00-1,87-2,41 0, ,18-1,91-2,08-1,86-1,65-2,03-1,91-1,68-1,56-1,50-1,83 0, ,77-0,65-0,71-0,62-0,50-0,70-0,64-0,53-0,45-0,42-0,60 0, ,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 h max 0,94 1,79 0,86 1,90 3,00 0,88 1,62 2,60 2,80 3,16 1,95 - h min -4,77-4,13-4,65-4,09-3,35-4,54-4,23-3,62-3,31-3,13-3,98 - Н 5,71 5,92 5,51 5,99 6,35 5,42 5,84 6,22 6,10 6,29 5,93 0,10 Table 12 - The deviation from the straight line connecting the extreme points of the SKS RSE KazInMetr bridge profile at each point of the bridge, obtained by means of the dedicated measuring system of SKS RSE KazInMetr 17

18 Point number Deviation from the line connecting the extreme profile point mean of measurement in µm Type A standard uncertainty 0 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 1-0,16 0,10 0,15-0,12 0,17 0,07 0,19 0,26 0,33 0,00 0,10 0,05 2-0,51 0,07 0,15-0,36 0,14-0,01 0,22 0,37 0,37-0,31 0,01 0,10 3 0,49 1,32 1,49 0,71 1,40 1,22 1,57 1,81 1,77 0,90 1,27 0,14 4 0,38 1,64 1,71 0,58 1,51 1,27 1,79 2,06 2,01 0,90 1,39 0,19 5 0,47 1,95 2,11 0,72 1,81 1,54 2,17 2,46 2,45 1,23 1,69 0,22 6 0,37 2,00 2,21 0,58 1,84 1,57 2,26 2,63 2,59 1,36 1,74 0,25 7 0,23 2,01 2,24 0,40 1,80 1,51 2,33 2,73 2,69 1,27 1,72 0,28 8-0,07 1,87 2,16 0,08 1,58 1,33 2,23 2,65 2,62 1,10 1,56 0,30 9-0,55 1,55 1,89-0,21 1,18 0,99 1,99 2,45 2,38 0,74 1,24 0, ,11 1,16 1,54-0,70 0,74 0,58 1,69 2,20 2,06 0,30 0,85 0, ,46 0,79 1,49-0,94 0,57 0,45 1,67 2,24 2,02 0,08 0,69 0, ,74 0,65 1,33-1,27 0,29 0,22 1,55 2,10 1,86-0,11 0,49 0, ,91 0,48 1,26-1,50 0,08 0,08 1,49 2,04 1,88-0,31 0,36 0, ,09 0,41 1,18-1,92-0,02 0,00 1,48 1,97 2,08-0,46 0,26 0, ,94 0,63 1,41-1,79 0,14 0,10 1,80 2,21 2,37-0,25 0,47 0, ,59 0,93 1,81-1,44 0,50 0,51 2,25 2,57 2,84 0,12 0,85 0, ,36 1,25 2,12-1,17 0,79 0,88 2,67 2,98 3,19 0,45 1,18 0, ,03 1,60 2,43-0,80 1,29 1,29 3,25 3,29 3,58 0,82 1,57 0, ,99 1,77 2,59-0,66 1,40 1,46 3,44 3,40 3,76 1,02 1,72 0, ,10 1,64 2,45-0,79 1,28 1,37 3,36 3,39 3,67 0,98 1,63 0, ,92 1,78 2,58-0,64 1,41 1,55 3,52 3,53 3,82 1,06 1,77 0, ,77 2,04 2,84-0,31 1,77 1,89 3,73 3,85 4,08 1,39 2,05 0, ,40 2,27 3,09 0,06 2,11 2,23 4,05 4,12 4,37 1,70 2,36 0, ,14 2,48 3,24 0,25 2,25 2,44 4,18 4,26 4,49 1,85 2,53 0, ,06 2,53 3,33 0,36 2,34 2,62 4,16 4,31 4,54 2,19 2,64 0, ,16 2,26 3,00 0,12 2,06 2,38 3,80 3,98 4,21 1,97 2,36 0, ,76 1,57 2,25-0,58 1,36 1,54 3,01 3,19 3,41 1,24 1,62 0, ,49 0,68 1,36-1,40 0,45 0,62 2,08 2,27 2,42 0,38 0,74 0, ,35-0,30 0,36-2,31-0,50-0,29 1,01 1,21 1,34-0,61-0,24 0, ,16-1,26-0,64-3,18-1,42-1,28 0,02 0,17 0,25-1,59-1,21 0, ,09-2,39-1,78-4,01-2,45-2,35-1,16-1,00-0,99-2,66-2,29 0, ,77-3,27-2,65-4,71-3,28-3,34-2,11-1,89-1,89-3,46-3,14 0, ,06-3,69-3,15-4,99-3,71-3,72-2,66-2,40-2,40-3,84-3,56 0, ,57-3,42-2,91-4,53-3,42-3,42-2,48-2,25-2,25-3,50-3,28 0, ,99-3,02-2,58-3,98-3,03-2,97-2,18-1,98-1,99-3,06-2,88 0, ,34-2,52-2,16-3,33-2,61-2,51-1,84-1,66-1,69-2,59-2,42 0, ,77-2,16-1,86-2,84-2,20-2,06-1,62-1,45-1,53-2,10-2,06 0, ,97-1,59-1,31-2,08-1,63-1,51-1,21-1,13-1,11-1,73-1,53 0, ,73-0,59-0,42-0,83-0,67-0,59-0,43-0,38-0,37-1,00-0,60 0, ,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 h max 0,49 2,53 3,33 0,72 2,34 2,62 4,18 4,31 4,54 2,19 2,64 - h min -5,06-3,69-3,15-4,99-3,71-3,72-2,66-2,40-2,40-3,84-3,56 - Н 5,55 6,22 6,48 5,71 6,04 6,34 6,84 6,71 6,94 6,03 6,29 0, The graph of the BelGIM bridge profile drawn from the measurements of each comparison participant is shown in Figure 7. 18

19 BelGIM Bridge Profile 1,00 Deviation from the straight line connecting the extreme 0,00 profile points, μm ,00-2,00-3,00-4,00-5,00-6,00 Point numbers BelGIM UNIIM SKS RSE KazInMetr Figure 7 The graph of the deviations from the straight line connecting extreme points of the Bel- GIM bridge 7.3 The graph of the UNIIM bridge profile drawn from the measurements of each comparison participant is shown in Figure. Deviation from the straight line UNIIM Bridge Profile connecting 22,00 the extreme profile points, 19,00 μm 16,00, 13,00, 10,00 7,00 4,00 1,00-2,00 Point numbers BelGIM UNIIM SKS RSE KazInMetr Figure 8 The graph of the deviations from the straight line connecting extreme points of the UNIIM bridge 7.4 The graph of the SKS RSE KazInMetr bridge profile drawn from the measurements of each comparison participant is shown in Figure 9. 19

20 SKS RSE KazInMetr bridge profile Deviation 4,00from the straight line connecting 3,00 the extreme profile points, 2,00 μm 1,00, 0,00-1, , -2,00-3,00-4,00-5,00 Point numbers -6,00 BelGIM UNIIM SKS RSE KazInMetr Figure 9 The graph of the deviations from the straight line connecting extreme points of the SKS RSE KazInMetr bridge 8 Procedure of evaluating the equivalence of the national standards included in the comparisons The of the measurements conducted by the comparison participants were verified by using the following two methods: - based on the En-criterion; - based on the degree of equivalence of the measurement standards d, u( d )) ( 8.1 Examination of measurement using the En-criterion method To evaluate the internal closeness between the individual measurement the En-criterion was applied. For k=2, En 1. E n 1 x xref (3) k u u 2 2 ref x ref n 1 n p 1 x p (4) u ref 1 n 1 1 u 2 (5) 20

21 1 p u 2 where x is the measurement result obtained by the -th laboratory; u is the standard uncertainty reported by the -th laboratory; p is the weight of the measurement result obtained by the -th laboratory; x ref is the reference value (weighted average) of the comparison; u ref is the standard uncertainty of the reference value; n is the total number of the comparison participants The values of the En-criterion for the BelGIM bridge are given in Table 13. (6) Table 13 Name of characteristic Measurement result of the laboratory, x, μm Total standard uncertainty reported by the laboratory, u, μm (k=1) Laboratory abbreviation BelGIM UNIIM SKS RSE KazInMetr 5,94 5,90 5,75 0,24 (0,08L ) 0,30 (0,10L ) 0,30 (0,10L ) Reference value (weighted average) of the comparison, xref, μm 5,88 Standard uncertainty of the reference value, uref, μm 0,159 En-criterion value 0,18 0,05-0,25 Note: L, m stands for the length of the BelGIM bridge (see Table 2). All values of the En-criterion for the BelGIM bridge obtained by the comparison participants are below the level specified: En The values of the En-criterion for the UNIIM bridge are given in Table 14. Table 14 Name of characteristic Measurement result of the laboratory, x, μm Total standard uncertainty reported by the laboratory, u, μm (k=1) Laboratory abbreviation BelGIM UNIIM SKS RSE KazInMetr 20,21 19,51 19,66 0,40 (0,08L ) 0,50 (0,10L ) 0,50 (0,10L ) Reference value (weighted average) of the comparison, xref, μm 19,86 Standard uncertainty of the reference value, uref, μm 0,265 En-criterion value 0,59-0,41-0,23 Note: L*, m stands for the length of the UNIIM bridge (see Table 2). 21

22 All values of the En-criterion for the UNIIM bridge obtained by the comparison participants are below the level specified: En The values of the En-criterion for the SKS RSE KazInMetr bridge are given in Table 15. Table 15 Name of characteristic Laboratory abbreviation BelGIM UNIIM SKS RSE KazInMetr Measurement result of the laboratory, x, μm 6,35 5,93 6,29 Total standard uncertainty reported by the laboratory, u, μm (k=1) 0,32 (0,08L ) 0,40 (0,10L ) 0,40 (0,10L ) Reference value (weighted average) of the comparison, xref, μm 6,22 Standard uncertainty of the reference value, uref, μm 0,212 En-criterion value 0,28-0,42 0,11 Note: L, m stands for the length of the SKS RSE KazInMetr bridge (see Table 2). All values of the En-criterion for the SKS RSE KazInMetr bridge obtained by the comparison participants are below the level specified: En Examination of measurement using the degree of equivalence method d, u( d )) ( The degree of equivalence d for the -th institute is defined as the deviation of the measurement result from the reference value and can be calculated by formula d x x, (7) ref where x ref is the reference comparison value derived by Formula (4). The uncertainty of the degree of equivalence, u(d ) can be calculated by formula u( d 2 2 ) u ( x ) u ( x ) (8) ref The minus sign shows up in Formula (6) due to correlation between the measurement result and the reference value computed with respect to that measurement result. The measurement standards are considered to be equivalent if the following condition is fulfilled: d u( d ) or (9) 2 d U d ) (10) ( 22

23 8.2.1 The of checking the degrees of equivalence for the BelGIM bridge are given in Table 16. Table 16 Name of characteristic Laboratory abbreviation BelGIM UNIIM SKS RSE KazInMetr Measurement result of the laboratory, x, μm 5,94 5,90 5,75 Total standard uncertainty reported by the laboratory, u, μm (k=1) 0,24 (0,08L ) 0,30 (0,10L ) 0,30 (0,10L ) Reference value (weighted average) of the comparison, xref, μm 5,88 Standard uncertainty of the reference value, uref, μm 0,159 Difference between the measured and reference value, d, μm 0,06 0,02-0,13 Standard uncertainty of the degree of equivalence, u(d), μm 0,18 0,25 0,25 Expanded uncertainty of the degree of equivalence U(d) 0,36 0,51 0,51 Note: L, m stands for the length of the BelGIM bridge (see Table 2). From Table 16 it is evident, that when comparing d and U(d ) the condition (10) is fulfilled, therefore the measurement standards being compared are considered equivalent The of checking the degrees of equivalence for the UNIIM bridge are given in Table 17. Table 17 Name of characteristic Laboratory abbreviation BelGIM UNIIM SKS RSE KazInMetr Measurement result of the laboratory, x, μm 20,21 19,51 19,66 Total standard uncertainty reported by the laboratory, u, μm (k=1) 0,40 (0,08L ) 0,50 (0,10L ) 0,50 (0,10L ) Reference value (weighted average) of the comparison, xref, μm 19,86 Standard uncertainty of the reference value, uref, μm 0,265 Difference between the measured and reference value, d, μm 0,35-0,35-0,20 Standard uncertainty of the degree of equivalence, u(d), μm 0,30 0,42 0,42 Expanded uncertainty of the degree of equivalence U(d) 0,60 0,85 0,85 Note: L, m stands for the length of the UNIIM bridge (see Table 2). 23

24 From Table 17 it is evident, that when comparing d and U(d ) the condition (10) is fulfilled, therefore the measurement standards being compared are considered equivalent The of checking the degrees of equivalence for the SKS RSE KazInMetr bridge are given in Table 18. Table 18 Name of characteristic Laboratory abbreviation BelGIM UNIIM SKS RSE KazInMetr Measurement result of the laboratory, x, μm 6,35 5,93 6,29 Total standard uncertainty reported by the laboratory, u, μm (k=1) 0,32 (0,08L ) 0,40 (0,10L ) 0,40 (0,10L ) Reference value (weighted average) of the comparison, xref, μm 6,22 Standard uncertainty of the reference value, uref, μm 0,212 Difference between the measured and reference value, d, μm 0,13-0,29 0,07 Standard uncertainty of the degree of equivalence, u(d), μm 0,24 0,34 0,34 Expanded uncertainty of the degree of equivalence U(d) 0,48 0,68 0,68 Note: L, m stands for the length of the SKS RSE KazInMetr bridge (see Table 2). From Table 18 it is evident, that when comparing d and U(d ) the condition (10) is fulfilled, therefore the measurement standards being compared are considered equivalent. 8.3 The of measurements of straightness deviations for the BelGIM bridge are shown in Figure

25 6,40 Results of measurements of straightness deviations for the BelGIM bridge BelGIM UNIIM KazInMetr 6,30 6,20 6,10 μm 6,00 5,90 5,80 Reference value 5,70 5,60 5,50 5,40 0 0,5 1 1,5 2 2,5 3 3,5 4 Figure 10 Results of measurements of straightness deviations of the BelGIM bridge. 8.4 The of measurements of straightness deviations for the UNIIM bridge are shown in Figure 11. Results of measurements of straightness deviation for the UNIIM bridge BelGIM UNIIM KazINMetr 20,80 20,60 20,40 20,20 20,00 μm 19,80 19,60 19,40 19,20 19,00 18,80 0 0,5 1 1,5 2 2,5 3 3,5 4 Reference value Figure 11 Results of measurements of straightness deviations of the UNIIM bridge. 25

26 8.5 The of measurements of straightness deviations for the SKS RSE KazInMetr bridge are shown in Figure 12. 6,80 Results of measurements of straightness deviation for the SKS RSE KazInMetr bridge BelGIM UNIIM KazInMetr 6,60 6,40 μm 6,20 Reference value 6,00 5,80 5,60 5,40 0 0,5 1 1,5 2 2,5 3 3,5 4 Figure 12 Results of measurements of straightness deviations of the SKS RSE KazInMetr bridge 9 Resume 9.1 The comparison indicate that the measurement uncertainties comply with the reported values. 9.2 The standards under comparison are equivalent. Bibliography [1] ISO/IEC Guide 98-3:2008 Uncertainty of measurement Part 3. Guide to the expression of uncertainty in measurement (GUM:1995). [2] COOMET R/GM/11:2010 Regulations for comparison of measurement standards from the national metrological institutes of CООМЕТ. [3] COOMET R/GM/14:2016 Guidelines for Data Evaluation of COOMET Key Comparisons 26